New posts in combinatorics

How to show that $\sum\limits_{k=0}^n (-1)^k\tfrac{{ {n}\choose{k}}}{{ {x+k}\choose{k}}} = \frac{x}{x+n}$

sequences-and-series combinatorics summation binomial-coefficients

Sum of reciprocals of binomial coefficients: $ \sum\limits_{k=0}^{n-1}\frac1{\binom{n}{k}(n-k)} $

combinatorics summation binomial-coefficients

Partition Generating Function

combinatorics generating-functions integer-partitions

Counting vectors in $\mathbb{Z}_n^n$ with $0$ as a most common coordinate value

combinatorics vectors combinations

Minimum multi-subset sum to a target

Prove $\sum_{i=0}^n (-1)^{n-i} \binom{n+1}{i} (i+1)^n = (n+2)^n$

calculus sequences-and-series combinatorics summation power-series

Find the sum of $\binom{2016}{4} + \binom{2016}{8} +\binom{2016}{12} + \dots + \binom{2016}{2016}$

combinatorics summation binomial-coefficients

Is the probability $\frac12$?

probability combinatorics

Lattice Paths that Avoid a Point

Calculating $\sum_{0\le k\le n/2} \binom{n-k}{k}$ [closed]

combinatorics sequences-and-series binomial-coefficients

How many ways can $b$ balls be distributed in $c$ containers with no more than $n$ balls in any given container?

Analysis of how-many-squares and rectangles are are there on a chess board?

What is the easiest way to find the number of triangles in this picture?

Accuracy of approximation to inclusion-exclusion formula in prime sieve

number-theory combinatorics prime-numbers analytic-number-theory sieve-theory

Find the highest power of two in the expression.

combinatorics elementary-number-theory discrete-mathematics

$\frac{1}{2^n}\binom{n}{n}+\frac{1}{2^{n+1}}\binom{n+1}{n}+...+\frac{1}{2^{2n}}\binom{2n}{n}=1$: short proof?

probability combinatorics summation combinations

There are $2n+1$ people. For each $n$ people there is somebody who is friend with each of them. Prove there is a "know-them-all" person.

combinatorics discrete-mathematics graph-theory contest-math

British Mathematical Olympiad - December 2001 - Round 1 - Question 4

combinatorics combinatorial-geometry

How many ways to merge N companies into one big company: Bell or Catalan?

combinatorics elementary-set-theory set-partition

The sum $\sum_{j=0}^n \binom{n}{j} \left\{ j \atop k \right\} x^j$

combinatorics binomial-coefficients recurrence-relations generating-functions stirling-numbers